Electronic structure model for single B, C or N adatoms upon graphite

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upon graphite

A. Rakotomahevitra, C. Demangeat, J. Parlebas, G. Moraitis, E.

Razafindrakoto

To cite this version:

A. Rakotomahevitra, C. Demangeat, J. Parlebas, G. Moraitis, E. Razafindrakoto. Electronic structure

model for single B, C or N adatoms upon graphite. Journal de Physique I, EDP Sciences, 1993, 3

(11), pp.2299-2309. �10.1051/jp1:1993246�. �jpa-00246869�

Classification

Physics

Abstracts

71.55-73.20

Electronic structure model for single B, C

_or

N adatoms _upon

graphite

A-

Rakotomahevitra(~),

C.

Demangeat(~),

J-C-

Parlebas(~),

G.

Moraitis(~)

and E.

Razafindrakoto(~)

(~)

I-P-C-M-S--G-E-M-M-E-

(UM

46

CNRS),

Universit4 Louis Pasteur, 67070

Strasbourg,

France

(~) Ddpartement

de

Physique,

Universitd Marien

Ngouabi, Brazzaville, Congo (~)

Laboratoire

d'Energdtique,

BP 906,

Ankatso,

Antananarivo,

Madagascar

(Received

17

February

1993, revised 11 June 1993, accepted 20

July1993)

Abstract. An extra-orbital

tight-binding

scheme and _a

repulsive Born-Mayer

model _are

used to determine the total

adsorption

_energy of _a

2p

adatom

(B,

C _or

N)

at the surface of

graphite.

The

corresponding

electronic structure of the adsorbed atom is deduced for the most

stable

(hollow) position.

Our model allows _us to exhibit _an increase of the local

density

of states _on the adatom and _a decrease of

charge

transfer

(from

adatom to

carbon)

when

going

from boron to

nitrogen.

1 Introduction.

Nitrogen

adsorbed _upon

graphite

is _one of the

adsorption systems

for which various exper- imental and theoretical results exist

[1-5]-

^Also

graphite

is _one of the most

commonly

used materials in

atomic-force-microscopy (AFM)

_[6] and

scanning-tunnelling-microscopy

_[7] studies of surface

morphology. Recently

_progress has been achieved in

molecular-dynamics

simulations of the metallic

tip-substrate

interaction in AFM

[8].

^{Also the} interaction

energies

between _a

sharp

Pd

tip

with _one apex ^atom and

graphite

_were ^studied _on the basis of

first-principle

cal- culations

[9, 10].

^{Moreover there is} a

general

interest in the

study

of the electronic structure of transition metal adatoms _upon

graphite

since

graphite

is _an ideal substrate for such

adsorbates;

for

example

_open

questions

_are ^{the conditions of} appearance of local

magnetic

moments at V adatoms

[11]

or also the

general

electronic structure trends

along

the 3d series of adatoms.

Because carbon

occupies

_a middle

position

in the order of

electronegativity

of the elements in the

periodic table, graphite

welcomes _many chemicals

(especially 2p

_or

3d)

_as adsorbates.

In the

present

_paper we restrict _our

study

to the electronic structure of

light 2p

atoms

(B, C, N)

adsorbed _upon

graphite,

at the

beginning

of

adsorption,

I-e- when isolated adatoms _pre-

dominate. More

precisely

_we ^focus _our attention _{on one}

(sixfold)

hollow adsorbed atom and _we

develop

a

simple

extra-orbital

tight-binding (EOTB)

model. The

simplicity

of the model based

on electron

sharing

between adsorbate and

substrate,

_as ^well as its self-consistent

screening

in

the _sense of Friedel

[12], permits

us to describe the trends in

chemisorption properties

^of the

adatoms

along

the

2p

series. It is also

interesting

^from an electronic

point

of view to com-

pare the

present adsorption-situation

to

previously

considered

single-impurity

intercalation- situation in bulk

graphite [13-15].

^{As for} an

adatom,

_a total _energy

calculation, taking

into account both band structure and

repulsive contributions,

is able to

provide

the _most stable

position

of the adsorbed

atom,

ⁱⁿ a

given geometrical position,

hollow for

example

in the

present

^{work. The actual adsorbate}

position

is

usually

^assumed to be the site with the

largest

coordination number

(here six)

available _on the surface. This _paper is

organized

_as follows:

in section 2 _we first calculate the band structure of _a

basal-plane

surface of

graphite

^within

the

tight-binding (TB)

method _as well _as the

corresponding

^intersite Green functions. Next

we

present

our EOTB

adsorption

model

(Sect. 3)

and _our method _to find out the most stable

(hollow) position

_upon

graphite

from _a total energy

computation (Sect. 4)- Finally (Sect. 5)

we exhibit and discuss _our numerical results for

B, C,

N adatoms.

2. Band structure of _a

graphite

surface.

Recently

the

interlayer

interactions within _a

bilayer

of

graphite

have been studied

using

local

density approximation [16].

It

happens

that the

interlayer

distance is

only

0.7 _To

larger

in

a

bilayer

than in the bulk

graphite;

also the intercarbon distance within _a

graphite layer

is

practically

the _same for _a

bilayer

and for bulk

graphite.

In the

present study

_{we assume} that

graphite

surface is well

represented by

_a

bilayer

of

graphite

within TB method. In this method the

parameters corresponding

to1r and _a bands

[13]

are fitted

[17].

^The

bilayer

is obtained

by disregarding

the further

hopping integrals

_n~2 and _n~5 in _a

bulk-graphite

model

[18].

^In our

band structure calculation _{we use} the

following hybridized sp~

atomic

orbitals, (lR), (2R), (3R)

built from linear combinations of

(sR), (xR), (yR)

and the

nonhybridized (4R)

orbital

just given by:

14fl)

₌

lzfl) (1)

Then,

the

density

of states

(DOS)

_per

spin

at _a carbon site R is

given

in _terms of the

bilayer graphite

Green function

G°(E)

ni(E)

₌

-(1/7r) ~

Im

Gti(E); Gti(E)

=

iii _{(E+ H°)}

^-~

ti) ₍₂₎

In

equation (2)

t

=

I,

A and H° is the

bilayer graphite

Hamiltonian. In order to determine the electronic structure of _an adatom

(next section)

_we also need to define and calculate intersite Green functions _as

[14]:

G(~(, (E)

=

(tR( (E+ H°)~~ ji'R') (3)

In _our numerical

application

_we consider 10 000

k-points

in the reduced Brillouin _zone

[15], keeping,

the

k-components parallel

to the

bilayer.

Our results for the carbon DOS of _a

graphite bilayer

is in fair

agreement

^{with reference}

[16].

^{It is}

interesting

to

decompose

the carbon DOS

(Fig. I)

into

(I)

air,contribution

(arising

from

(4R) orbitals)

which is

unique

in the

vicinity

E

~

E

j

I

l

~

2 _o pi

ul

O

C

-20

ENERGY

(eV )

Fig.

1- Density of states

(DOS)

of

a bilayer ^of

graphite: x(- -)

and

a(-)

contributions.

of the Fermi level

(EF

= -0.05

eV),

and

(it)

_a a-contribution which is also

unique

at

higher energies.

At intermediate

energies

both _a and1r

symmetries

contribute.

3. Electronic

adsorption

model.

The EOTB Hamiltonian for _an adatom A _on

graphite

is then written _as H

= H° ₊ the

following

terms:

~ _{'lll~) ~i (lll~'}

₊

~ ('lll~) fli~

(i~~~' ~

~.C.)

^~

~ _'~~)

_~~~R

(~)

_(i~~~'

(~)

m Rtm Rt

in

equation (4), Et

^is the energy level introduced

by

the adsorbed orbital

(mA)

at site A at a distance h

abovilthe graphite

surface with the atomic orbital

symmetry

m = s, x, y, ^z for adatoms

belonging

to the

2p series; flf(

is the

hopping integral

between the adsorbed atomic orbital

(mA)

and _a

surrounding

carbon molecular orbital

(tR) (t

=

1, 4)

it is

expressed

in terms of Slater-Koster atomic

hopping integrals _[19].

In the last term of

equation (4)

V(t~ (A) designates

the additional

perturbation potential

at carbon site R due to the

adsorption phenomenon.

From _a numerical

point

of view

(see

Sect.

5) Et

and

V(t~ (A)

will be determined for _a

given

h from:

(i)

the Friedel _sum rule which is

expressed

in terms of

Gh(E),

the

perturbed

Green function associated to H

2

Zh (EF)

"

Ni> ⁽⁵⁾

Zh

jE)

=

-11 /7r)Im /~

lY

(Gh iE') G°(E')) ^dE' (6)

with

N(

₌

3, 4,

5

corresponding respectively

to the number of external _s and _p electrons

brought by

A

=

B, C, N,

and with

Zh(E) defining

the total number of

displayed

states per

spin,

_up to the _energy

E,

after the

adsorption

of _an A atom at _a distance h above the

graphite

surface.

ii)

the local

neutrality

_on the cluster

AC6

when A

occupies

_a hollow

position

_{upon a} carbon

hexagon

of

graphite:

E~ ⁶

2

/ _fifA(E)

+

~j 6fifR(E)

dE

=

N( (7)

R=1

In

equations (5)

and

(7)

the factor 2 stands for the

spin degeneracy

and the local DOS

(LD OS)

per

spin

at site A is defined

by:

fifA(E)

=

(-1/1r)Im ~j _{Gii(E), (8)}

whereas the variation of the LDOS at _a carbon site R due to the

adsorption

is:

~M~(E)

=

(-i/~r)

im

~ _(Gj~(E) Gjj(E)) (g)

i

Actually

within _a first order

expansion

in terms of

V(~~ (A),

it is

quite

_easy to

explicit

the

perturbed

Green functions of

equation (8):

it is _a

straightforward

extension of

equations (2.2), (2.3)

and

(2A)

in reference

[15].

^{A similar}

expression

^{has been derived for}

6fifR(E)

in equa-

tion

(9) [20].

4. Total

adsorption

_energy.

There is _an

interesting point

in the

adsorption problem:

the exact

height

h of the adatom A above the

graphite

surface is determined

through

_a total _energy calculation

corresponding

to the

adsorption

_process of atom A. The

general

definition

[21]

^{of the total}

adsorption

_energy

Ead(h)

of _an A atom at _a distance h above

graphite

is

given by

_{a sum} of

(I)

_an attractive

(band

contribution) Ebs(h)

term,

(it)

an electronic Coulomb term

Eee(h)

which has to be subtracted because it has been counted twice in

Ebs(h)

and

(iii)

a

repulsive (Born-Mayer contribution) Er(h)

term:

Ea~(h)

=

E~~(h) E~~(h)

+

E~(h) (io)

The band structure term can be written _as follows with _an evident notation:

Ebs(h)

= E

(A/graphite)

E

(A) E(graphite) (11)

After _a bit of

manipulation, Ebs

_can be cast into the

following

form:

Ebs(h)

= 2

EF Zh (EF)

2

/

^~~

_Zh(E)

_dE

_{~j N(~EQ (12)}

~

where

N(~

is the electron number of

symmetry

_m

brought by

the adatom A and

Em

is the

corresponding

atomic level. The electronic Coulomb term is

given by

the

following expression

[22, 23]:

Eee(h)

₌

~j _{U( bN((h) N(~}

₊

_{~bN((h) (13)}

in

~

bNl(h)

_"

Nl(h) Nl~

~ _"

IA> Rj

_n

=

js, pj ₍₁₄₎

where

bN((h)

is the variation of the local electron number _at site I and of

symmetry

n due to the

adsorption,

whereas

N((h)

is the local electron number after

adsorption

of A within _a distance h. Also

U(

is the intrasite Coulomb _energy between two n electrons at site I. The

repulsive

term

Er(h)

_can be

phenomenologically represented by

_a

Born-Mayer potential:

it describes at short distances the ion,ion

repulsive

interaction between the A atom and the

neighbouring

carbon _atoms of the

graphite

surface. The

general phenomenological

form of

Er

is written _as follows

[24]

ⁱⁿ terms of the

height

h of the adatom above

graphite:

Er(h)

= a

exp(-a h) (15)

where _a and _{a are} the parameters of the

Born-Mayer potential

which characterize each

type

of

adsorption.

For

example

in the _case of _an adsorbed carbon atom upon

graphite

_a

= 208 eV

and _a

= 3.3

(I)~~ _according

_to reference

[25].

^For

simplicity

and due _{to a} lack of

data,

in the

following _section,

_we will

keep

the above carbon

parameters

also for boron and

nitrogen adatoms,

since these elements _are close

by

in the classification table. Of _course the

equilibrium position ho

of the adatom

corresponds

to the _energy minimum of

Ead(h)

_{as we} will _see in the next section.

5. Numerical results and discussion.

The

hopping integrals (flf() appearing

in

equation (4)

are calculated

according

to references

spa, ppa and

_pplr [19]. _We also scaled

the

^ntegrals _in rder

to be

_{able to}

in pure graphite [20].

The

ifference of energy _levels

E[

- E[ _(see Eq. (4))

which characterizes

the adatom

A is

taken from _{lementi [26].} The

value

U[ (= U[) for

nitrogen is

2.39 eV cording to reference [21]. The rresponding values for

boronand ^arbon

are

^educed

from that

for

itrogen,proportionally

to

the

atomic

values [27]. The ratio of _the corresponding

perturbation potentials ^((A)/V((A)

(see Eq.

(4) with V(~~ (A)

e

V((A) on a eighbouring

graphite site) is

ssumed

to be

given

by the

ratio

of

_the

rystal

field

calculated

similarly to the opping ntegrals. Finally

we

end up _with two unknown variables

E[

and

V((A)

: they

are

self-consistently determined_throughequations (5) and (7) as explained

in

section

_.

This

_is

true

for

a given

^eight h

of

_A

right

toms. The _last step _{of our}

omputation is

to find

_out the ^ost

stable

_height

to

a _minimum of

the

_total

adsorption

energy.

To do this the zero of energy

is assumed

to

level. _Next the _graphite

band

_is ^ocated so as to _satisfy theexperimental ^ork function

value for graphite [28]

;

in

this case _the

Fermilevel

is

at

-5

^eV. Then

Em of

equation ₍₁₂₎

_also taken _from

Clementi [26]. Figure 2 our results of

the

_total

adsorption

_energy for B, C and N datoms.

The

ost stable _heights ho are

0.85 I

and

_1.06 I _(see

also Fig. _3a) which

correspond to distances

between

the _adatom ^and

the ^aphite carbon _neighbours f1.74

I,

1.65

I and

^1.77

I

(Notice that the

C-C

8hortest

distance

within

a ^xagon in ^aphite is 1.42

I whereas in

the ntercalation

(

_a

) ^BORON

1.02 A

o.80

( b ) CARBON

Ms

>

aJ 0.85 A

_

~_ O.80 DO 20

~j

©~

$ 2~

~Z~

(

_c

) NITROGEN

I-OS A

o.8a 1-no

Distance above

graphite ^surface (Al

Fig- 2- Total

adsorption

_energy for _a boron

(a), carbon(b)

_or

nitrogen (c)

adatom

(hollow position)

with respect to its distance above

graphite

surface.

of Refs.

[14, 15]

^{the two first carbon}

neighbours

of _an interstitial atom are at 1.83

I

_{and the}

four next nearest at 2.09

I).

_{Moreover the}

_charge

transfer from A toward the

graphite

carbon

neighbours

is

decreasing along B,

C and N

(Fig. 3b).

This

suggests

_a

change

in

chemisorption

from _a rather

strong coupling

situation in the _case of boron to a rather weak

coupling

situation

(a ₎

~

~

.

i

_,'

#

~i

p6

~o "

B

(bj

t O

"~

#

~ ,

2 _',

[

O ,

i~ '.~

fl ~~

~J

B c N

Adsorbate

Fig.

3. -Distance above

graphite (a)

and

charge

transfer ratio

MG/N(

from the adatom _to the

graphite

carbon atoms

(b)

with respect to the considered adsorbate

(B,

C,

N).

in the _case of

nitrogen.

For the most stable hollow

positions,

it is

interesting

to exhibit the

corresponding

LDOS for

boron,

carbon and

nitrogen

adatoms

(Fig. 4).

In all three _{cases as} in the intercalation _case

[15],

^{there is} a

strong

^{virtual bound} state

(vbs)

at the Fermi

level,

the

origin

of which is

essentially 2p~

and

2py

note that these two contributions _{are not}

strictly

identical from

symmetry

reasons between _x and _y within _a

hexagon

of carbon atoms. However since the difference between _x and y is

small,

we exhibit _{x +} y on one hand and _z in the other

(Fig. 5).

The vbs _at

EF

is less filled for boron

(Fig. 4a)

and rather filled for

nitrogen (Fig. 4c).

Also in the three _cases of

figure

4 due _{to a}

corresponding strong

adsorbate-substrate

hopping integral

there is _an extended s bound state below the

graphite

band

[20]

^the

filling

of which

increases from boron _to

nitrogen.

Our main numerical results _are summarized in table I.

In this _{paper we} have studied the most stable

(hollow) position

of _a

2p light

adatom

(B, C, N)

_upon

graphite

surface

by using

_a total

adsorption

_energy calculation.

Although

_our EOTB

approach

^for the band _structure contribution is

quite crude,

we are sure to

satisfy

the Friedel

sum rule _as well _{as a} local

neutrality

condition _on the adatom and its first

graphite

carbon

neighbours.

Our model allows _us to exhibit _an increase of the local

density

of states _on the adatom and _a decrease of

charge

transfer

(from

adatom to

carbon)

when

going

from boron to

a)

_E

~/ b )

_E CARBON

E

^~

~ j

I

~

(

-20

ENERGY (eV

Fig. 4. Local density of states

(LDOi)

_of

a boron

(a),

carbon

(b)

and

nitrogen (c)

adatom upon

graphite

at the most stable

(hollow) height.

The Fermi level

(EF

" -0.05

eV)

is visualised

by

_a dashed

line. The _s bound state below the

graphite

band is

represented by

_a thin

straight

line.

nitrogen.

The

pre8ent

calculation will be extended to the _case of transition metal adatoms _upon

graphite

for which there is a number of

interesting experimental

data. Another

interesting

(

_~

)

z,

^BORON

(

_~

)

z,

^BORON

x+ y

z

~+

>

~ )

z,

^CARBON

( h )

z,

^CARBON

I '1

x+ y

z

~

~

+4

q/

ill

O

" "

Cl

-J

(

_~

)

z,

^NITROGEN

(

_~

)

z,

^NITROGEN

x+ y

z

-20 -lo 0 lo -20 -20 -lo 0 lo -20

ENERGY ( eV

Fig.

5. Contributions of

(p~

+

py)

and pz orbitals to the local

density

of states

(LDOS)

of _a boron

(a),

carbon

(b)

and nitrogen

(c)

adatom _upon

graihite

_{at the most stable}

_{(hollow) position.}

extension of the

present

model would be to describe the evolution of the electronic

adsorption

of _one

given

element when

going

from _one

single

adatom

(as

is the _case in the present

paper)

to one

single overlayer

with

possible

metallization _upon

graphite.

These

investigations

_{are now}

under progress.

Table I- The most stable

height

ho of adatom

A, corresponding

distance

do (bond length )

to each of the carbon atoms of the considered substrate

hexagon, perturbation potentials Vi

on the six

graphite

carbon

neighbours

of

A,

final

charge MA

_upon

A,

final

charge

transfer

MG

onto the six

graphite neighbours

of A after

adsorption, charge N( initially brought by

A with A =

B, C, N,

_{s energy} level introduced

by

the adsorbed

(sA) orbital,

intrasite Coulomb _energy

U[

between two p electrons at site A-

A Carbon

ho (I)

1.02 0.85 1.06

do (I)

_{1.74 1.65 1.77}

V((A) (eV)

0.22 0.05 -0-01

MA

_" 2

/~~ ^fifA(E)

^{dE 1.14 2.69 3.63}

MG

₌ 2

/ ^f _6fifR(E)

_{dE 1.86 1.31 1.37}

~~~

3.00 4.00 5.00

(eV)

7.60 -4.32 -11.38

U[ (= U[) (eV)

1.42 1.89 2.39

Acknowledgements.

The authors would like _to thank the referees for their

pertinent

remarks.

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L-W-, Pllys.

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3140.

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T-H-M- and Van der Avoird

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